gif_cond_exp_multisynapse is the generalized integrate-and-fire neuron according to Mensi et al. (2012) and Pozzorini et al. (2015), with post-synaptic conductances in the form of truncated exponentials.

This model features both an adaptation current and a dynamic threshold for spike-frequency adaptation. The membrane potential (V) is described by the differential equation:

where each eta_i is a spike-triggered current (stc), and the neuron model can have arbitrary number of them. Dynamic of each eta_i is described by:

tau_eta_i*d{eta_i}/dt = -eta_i

and in case of spike emission, its value increased by a constant (which can be positive or negative):

eta_i = eta_i + q_eta_i (in case of spike emission).

Neuron produces spikes STOCHASTICALLY according to a point process with the firing intensity:

lambda(t) = lambda_0 * exp[ (V(t)-V_T(t)) / Delta_V ]

where V_T(t) is a time-dependent firing threshold:

V_T(t) = V_T_star + gamma_1(t) + gamma_2(t) + ... + gamma_m(t)

where gamma_i is a kernel of spike-frequency adaptation (sfa), and the neuron model can have arbitrary number of them. Dynamic of each gamma_i is described by:

tau_gamma_i*d{gamma_i}/dt = -gamma_i

and in case of spike emission, its value increased by a constant (which can be positive or negative):

gamma_i = gamma_i + q_gamma_i (in case of spike emission).

Note that in the current implementation of the model (as described in [1] and [2]) the values of eta_i and gamma_i are affected immediately after spike emission. However, GIF toolbox (http://wiki.epfl.ch/giftoolbox) which fits the model using experimental data, requires a different set of eta_i and gamma_i. It applies the jump of eta_i and gamma_i after the refractory period. One can easily convert between q_eta/gamma of these two approaches: q_eta_giftoolbox = q_eta_NEST * (1 - exp( -tau_ref / tau_eta )) The same formula applies for q_gamma.

On the postsynapic side, there can be arbitrarily many synaptic time constants (gif_psc_exp has exactly two: tau_syn_ex and tau_syn_in). This can be reached by specifying separate receptor ports, each for a different time constant. The port number has to match the respective "receptor_type" in the connectors.